This works is dedicated to study of magnetic flux properties in thin-film superconductors. At present time superconductors are widely used in various micro- and nanoelectronic devices, for example, extremely sensitive magnetic field detectors, high-frequency generators with a very low noise and even as small ideal contacts. However at certain conditions thermomagnetic instrability can arise in such devices leading to serious malfunction. The model describing this process is presented in the thesis. It is shown that thermomagnetic or flux instability results in an abrupt formation of magnetic dendrites. Proposted model is based on solving the thermal diffusion and Maxwell equations taking into account nonlocal electrodynamics in the film and its thermal coupling to the substrate. Within this model the formation of the dendrites in thin-film superconductors is fully explained. Threshold magnetic and electrical fields corresponding to formation of dendrites are theoretically calculated and their dependence on termperature and superconductor dimensions turned out to be in excellent agreement with various experiments. Further detailed comparison of experimental data and theoretical results shows that the model is well suited for predictions and it is demonstrated that dendritic instability can be suppressed for sufficiently narrow strips, which is of particular importance for design of superconduction electronic devices. <br>
Recently it has been shown that superconductiing films patterned with dots and antidotes allow trapping of significant amount of magnetic flux. Moreover it is possible with the help of special antidote arrays to guide the motion of magnetic vortices over the film area, which opens up a new field often called fluxonics. General problem concerning maximum quantity of lux quanta trapped by one antidote (or simply hole)is described in the second part of the thesis. Current and magnetic field distrbutions along with flux saturation number are calculated by solving the London equation for the thin-ring gemometry. Saturation numbers for film and bulk superconductors have been compared and it is found that for large hole radius, the ration between results in bulk and film is proportional to square root of the hole radius. In the limit of small hole bulk and film superconductors can trap equal amoutn of flux. Knowing the saturation number, one may predict the interaction between vortices and antidot arrays in various experimental configurations.

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Paper 1. D.V. Denisov, A.L. Rakhmanov, D.V. Shantsev, Y.M. Galperin and T.H. Johansen, Dendritic and uniform flux jumps in superconducting films, Phys. Rev. B 73, 014512 (2006). The paper is not available in DUO. The published version is available at: http://dx.doi.org/10.1103/PhysRevB.73.014512

Paper 3. D.V. Denisov, D.V. Shantsev, Y.M. Galperin and T.H. Johansen, Flux saturation number of superconducting ring, arXiv:0709.1086 [cond-mat.supr-con]. The paper is not available in DUO. The arXiv version is available at: http://arxiv.org/abs/0709.1086